God cannot lie because it violates His nature.
I think Einstein and Nels Bohr settled the argument of people putting limitations on God. God is beyond rationality. Therefore the tools of rationality (argument) are inappropriate in the discussions. Believing is also not part of rationality. The idea of whether or not God could lie, presupposes that we could understand the mind of God. I stop at the idea we could fully and wholly understand the mind of God, and make a judgement.
Not sure if there is much more to say on the topic.
DK